There are several similar terms in Dwarf Fortress that are used to describe both the skill used to wield a weapon and the wielder themselves. All weapon skills determine in large part the accuracy and the damage inflicted when using a weapon of that type (along with the quality and material of that weapon).

Different races use different but similar terms for identical weapon skills. These terms, like "axedwarf" or "spearman", may vary between Fortress mode and Adventurer mode, but are the same skills except for the race of the creature wielding the weapon. However, whether macedwarf, maceman, macegoblin, mace-elf, or macewombat, they all refer to the same skill - in this case, with a mace or "mace-type" weapon. There is absolutely no difference in the skill itself, except that it seems odd to refer to a sword-wielding dwarf as a "swordsman". Especially in Fortress Mode, Dwarf Fortress is (oddly enough) heavily prejudiced in favour of dwarves, proudly so and unashamed of it, and so often the skills are all informally used in the ____-dwarf form. Formally or informally, any other race could be inserted - hammergoblins or markselves, etc.

Note that when Activated as a soldier, a dwarf will be called a recruit if they have no weapon (or wrestling) skill of 1 or greater, but otherwise will be called by their highest weapon skill regardless of what weapon they are actually carrying.

Different races are sometimes restricted to which weapons within a group they can use. Dwarves in Fortress Mode are limited to only using dwarf weapons; dwarfs in Adventurer Mode can use a much wider variety of other weapons with the same skill. (See specific weapons for more info.)

The weapon skills are:

Axeman/Axedwarf - using an axe-type weapon. This skill is separate from wood cutting.

Hammerman/Hammerdwarf - using a hammer-type weapon. Crossbows are considered a "hammer-type weapon" only when used in melee, rather than firing at range.

(* The crossbow and bow are sufficiently different as a weapon and skill to deserve their own article - See crossbowman, crossbow & related articles for a full discussion.)

Also, theoretically:

Blowgunner - using blowguns. However, no player-race in Dwarf Fortress begins able to learn skill nor the ability to make the weapon nor the ammo, so it has to be modded into the game. See Blowgun.

Special:

Mining - using a pick. Since miners typically reach Legendary skill rather quickly, this makes them a very effective fighting force early on despite a pick being an "inferior" weapon, as (as was mentioned above) skill level heavily influences damage.